Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 5

(i) $z_1+z_2$

If $z_1=7\left(\cos\dfrac{23\pi}{12}+i\sin\dfrac{23\pi}{12}\right)$ and $z_2=11\left(\cos\dfrac{11\pi}{12}+i\sin\dfrac{11\pi}{12}\right)$ then find the following and express the result into $x+iy$ form:

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(i) z1+z2z_1+z_2

z1=7(6+2)4−7(6−2)4iz_1=\frac{7(\sqrt{6}+\sqrt{2})}{4}-\frac{7(\sqrt{6}-\sqrt{2})}{4}i z2=−11(6+2)4+11(6−2)4iz_2=-\frac{11(\sqrt{6}+\sqrt{2})}{4}+\frac{11(\sqrt{6}-\sqrt{2})}{4}i z1+z2=−(6+2)+(6−2)i\boxed{z_1+z_2=-(\sqrt{6}+\sqrt{2})+(\sqrt{6}-\sqrt{2})i}

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